1. INTRODUCTION

With the development of fabrication techniques and integrated optics, the dimensions of photonic devices to be integrated have decreased by several orders of magnitude. However, due to the diffraction limit, the optical mode size and physical device dimensions of those photonic devices are restricted to being larger than half the wavelength of the optical field, and it remains a key fundamental challenge to realize all kinds of photonic devices that can break the diffraction limit.

The optical cavity, a versatile element for integrated optics, can be used in optical sensing [1], light sources [2], optical filters [3], optical modulators/switches [4], nonlinear optics [5], etc. Among them, dielectric whispering gallery mode microcavities can be used for highly sensitive detection of single biological or chemical molecules [6,7]; nevertheless, the sensitivity is not high, due to the fact that the energy is predominantly confined inside of the cavity body. These pure dielectric microcavities exhibit a high quality factor (${10}^{10}$) but require a relatively large size, which not only increases the physical dimensions but also tends to introduce a large mode volume (dozens of cubic micrometers). On the other hand, the surface plasmon polarition (SPP) is an electromagnetic excitation existing on the interface between the dielectric and metallic media; it has both the speed of photonics and also the scale of the electronics. Moreover, it has the ability to concentrate and channel electromagnetic energy below the so-called diffraction limit. Therefore, plasmonic microcavities with ultrasmall mode volume attract a lot of attention [8–10]. The problem is that the metal absorption loss is high. Recently, hybrid plasmonic microcavities have been proposed as a good option for realizing a relatively high $Q$ factor as well as nanoscale light confinement. Furthermore, hybrid microcavities have considerable energy distributed in the surrounding dielectric. Thus, they are accessible outside the structure for sensing purposes. In addition, people have recently developed various hybrid plasmonic microcavities based on the traditional hybrid plasmonic waveguide [11–18], e.g., a hybrid plasmonic nanodisk [12], hybrid plasmonic submicron-donut resonator [13], etc.

In this paper, we introduce a novel silicon hybrid plasmonic microring resonator that consists of a silicon-on-insulator (SOI) ring with a metal nanoring on the top. The mode properties such as $Q$ factor, mode volume, energy ratio, and sensitivity are investigated by employing the finite-element method (FEM) and analyzed considering the varying structure geometry. One of the unique features of this hybrid microring resonator is the high sensitivity of $\sim 497\mathrm{nm}/\mathrm{refractive}$ index unit (RIU). Moreover, for such a structure, the fabrication is simple and CMOS-compatible.

2. DEVICE STRUCTURE

Figure 1(a) depicts the proposed silicon hybrid plasmonic microring resonator. It is composed of a metal nanoring and a SOI ring. The metal nanoring and the silicon ring are coaxial, and the former is placed well on the latter; that is, they have the same major radius $R$. In the following study, $R$ is set to 5 μm, which is a typical size used in many hybrid plasmonic microcavities. The metal nanoring can be chemically synthesized with major radius $R$ and minor radius $r$ [19,20]. The width and the height of the silicon ring are denoted as $w$ and $h$, as shown in Fig. 1(b), which illustrates the cross section of the proposed silicon hybrid microring resonator. At the same time, we want to get an operating wavelength of 1550 nm, which is one of the most used windows, so the permittivities of silicon (Si), metal (the medium of the metal nanoring is assumed to be Ag due to its low metal absorption loss), and silica (${\mathrm{SiO}}_2$) are set to be ${\epsilon }_{\mathrm{Si}}=12.25$, ${\epsilon }_{\mathrm{Ag}}=-129+3.3i$, and ${\epsilon }_{{\mathrm{SiO}}_2}=2.25$ [21], respectively. The surrounding medium is air, whose dielectric constant is 1.0.

 

Fig. 1. (a) Structure of the proposed hybrid plasmonic microcavity, (b) the cross section, and (c) the field intensity distribution of the proposed hybrid plasmonic microcavity.

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For the proposed hybrid plasmonic microresonator, the metal nanoring on top of the SOI ring results in a hybrid plasmonic mode; this is because of the coupling between the SPP whispering gallery mode and the dielectric whispering gallery mode. To intuitively exhibit the hybrid plasmonic mode, we first resort to the FEM [22]. Figure 1(c) shows the field intensity distribution of the whispering-gallery-like hybrid plasmonic mode. As can be seen in Fig. 1(c), the hybrid plasmonic microcavity has considerable energy distributed in the surrounding dielectric. This result can be explained the hybrid mode, which attracts part of the cavity energy from the silicon ring microcavity. Furthermore, since the contact area between the silver nanoring and the silicon ring microcavity is small, the electromagnetic field of the hybrid plasmonic mode is highly confined around the interface of the silver nanoring and the silicon ring microcavity, resulting in subwavelength mode confinement. In general, the hybrid mode can be classified with only the azimuthal mode number $M$.

3. SIMULATION RESULTS

Now we investigate some parameters influencing the device properties by employing the FEM. We fix the height of the silicon ring $h=300\mathrm{nm}$, but vary the radius of the nanoring $r$ from 25 to 200 nm. The width of the silicon ring is set at $w=200$, 300, 400, 500, and 600 nm, respectively.

The $Q$ factor associated with the photon lifetime and the effective mode volume of the proposed plasmonic microresonator are important to fully understand the characteristics of the hybrid plasmonic mode. The $Q$ factor can be evaluated as [23]

Figure 2(a) shows the $Q$ factor for the hybrid modes. If one looks at the modes with the same $w$ value, as $r$ increases from 25 to 100 nm, the $Q$ factor clearly increases due to the reduced radiation loss, which indicates that the coupling between the SPP whispering gallery mode and the dielectric whispering gallery mode becomes weak and the hybrid mode gradually tends to the pure dielectric whispering gallery mode. As $r$ increases further, however, the $Q$ factor increases only slightly. If one looks at the modes with the same $r$ value, the calculated results show that a larger $Q$ factor is associated with a larger width of the silicon ring. This is because there is stronger confinement for a hybrid plasmonic microcavity with a larger $w$ value. In addition, a $Q$ factor as high as 600 can be achieved. In Fig. 2(b), we find that for the same $r(w)$ value, when $w(r)$ increases, the trend for the effective mode volume is similar to the trend for the $Q$ factor. The effective mode volume is as small as $0.15{\mathrm{\mu m}}^3$, which is much smaller compared to $10{\mathrm{\mu m}}^3$ in [23].

 

Fig. 2. Mode properties of the hybrid plasmonic modes versus width $w$ and radius $r$.

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To characterize the hybrid mode in more detail, we calculate the energy ratio $\eta$, which is defined as the ratio of energy outside the silicon region is and given by [24]

This hybrid microcavity may have potential applications in a refractive index sensor. The sensitivity $S$, defined as

The performance of the proposed silicon hybrid microresonator sensor, according to the figure of merit defined in above ($S=497\mathrm{nm}/\mathrm{RIU}$), is superior to the performance of a ${\mathrm{Si}}_3{\mathrm{N}}_4$-based microdisk with a radius of $R=15\mathrm{\mu m}$ that has a sensitivity of $S=22.8\mathrm{nm}/\mathrm{RIU}$ [25], a glass-based microring resonator with a radius of $R=60\mathrm{\mu m}$ that has a sensitivity of $S=141\mathrm{nm}/\mathrm{RIU}$ [26], and a hybrid plasmonic refractometer with a radius of $R=10\mathrm{\mu m}$ that has a sensitivity of $S=298\mathrm{nm}/\mathrm{RIU}$ [15]. It also can be seen that the proposed hybrid microresonator has a smaller size compared to these structures. Thus the proposed hybrid microresonator provides potential for ultracompact sensing applications with high sensitivity.

Next, we investigate the characteristics of the proposed hybrid plasmonic microring resonator varied with height $h$ of the silicon ring. Here, the radius $r$ and the width $w$ are set to 25 and 200 nm, respectively. Figure 3 plots the $Q$ factor, effective mode volume, energy ratio, and sensitivity as the height $h$ increases from 150 to 600 nm. From this figure, one sees that the $Q$ factor and the effective mode volume increase together as the height $h$ increases from 150 to 350 nm, while the energy ratio and sensitivity decrease together as the height $h$ increases from 150 to 350 nm. This is because there is more power confined in the silicon region, which indicates that the hybrid mode gradually tends toward the pure dielectric whispering gallery mode. As $h$ increases further, however, the $Q$ factor, mode volume, and sensitivity are not sensitive to $h$. In addition, calculations show that the ranges of the $Q$ factor, effective mode volume, and sensitivity are not great, in contrast to that of the height $h$. Therefore, in practice slight changes of the height $h$ during the fabrication of the device do not seriously affect the performance.

 

Fig. 3. Mode properties of the hybrid plasmonic modes versus height $h$.

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4. CONCLUSIONS

In conclusion, we have studied the hybrid plasmonic mode in a novel Si-based hybrid plasmonic microcavity consisting of a silver nanoring on top of a SOI ring. The hybrid modes are theoretically demonstrated to possess a very high $Q$ factor and extremely small mode volume. A $Q$ factor as high as 600 and an effective mode volume as small as $\sim 0.15{\mathrm{\mu m}}^3$ are achieved. In addition, the microcavity can be further engineered to be applicable for ultracompact sensing applications, with a high sensitivity of $497\mathrm{nm}/\mathrm{RIU}$ at the deep subwavelength scale.